Question

Suppose an engine's pv-diagram takes a rectangular path around pressures 104 kpa and 212 kpa and volumes 0.6 m³ and 2.2 m³. Calculate the engine's efficiency if the gas is monatomic.

Answer 1

The efficiency of the engine can be calculated using the formula Efficiency = 1 - (V2/V1)^(y-1), where V1 and V2 are the initial and final volumes, and y is the heat capacity ratio of the gas. For a monatomic gas, the heat capacity ratio is equal to 5/3. Substituting the given values, the efficiency of the engine is approximately 0.276.

Step-by-step explanation:

The efficiency of an engine can be calculated using the formula:

Efficiency = 1 - (V2/V1)(y-1)

where V1 and V2 are the initial and final volumes, and y is the heat capacity ratio or adiabatic index of the gas.

In this case, the engine's pv-diagram takes a rectangular path, which means that the heat capacity ratio is equal to the number of degrees of freedom plus one, since the gas is monatomic. For a monatomic gas, the heat capacity ratio y is equal to 5/3.

Plugging in the given values into the formula:

Efficiency = 1 - ((2.2 m³)/(0.6 m³))(5/3-1)

Simplifying the expression:

Efficiency = 1 - (2.2/0.6)(2/3)

Calculating the value:

Efficiency ≈ 0.276